Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7744/54,9942/214
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 7744,9942
Greatest Common Factor of Numerators i.e. GCF of 7744,9942 is 2 .
LCM of Denominators means LCM of 54,214 as per the given fractions.
LCM of 54,214 is 5778 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 7744,9942
2 | 7744, 9942 |
3872, 4971 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 7744
List of positive integer factors of 7744 that divides 7744 without a remainder.
1,2,4,8,11,16,22,32,44,64,88,121,176,242,352,484,704,968,1936,3872,7744
Factors of 9942
List of positive integer factors of 9942 that divides 9942 without a remainder.
1,2,3,6,1657,3314,4971,9942
Greatest Common Factor
We found the factors 7744,9942 . The biggest common factor number is the GCF number.
So the greatest common factor 7744,9942 is 2.
Lets's calculate LCM of 54,214
2 | 54, 214 |
27, 107 |
∴ So the LCM of the given numbers is 2 x 27 x 107 = 5778
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5778
Therefore, the GCF of Fractions 7744/54,9942/214 is 2/5778
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 54,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,214) x common factors =2 x 1 = 2
LCM(54,214) = ( 54 × 214 ) / 2
LCM(54,214) = 11556 / 2
LCM(54,214) = 5778
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
2. What is the GCF of Fractions for 7744/54, 9942/214?
Answer: GCF of Numerators as per given numbers 7744/54, 9942/214 is
GCF of Numerators i.e. for 7744,9942 is 2
LCM of denominators i.e. for 54,214 is 5778.
Thus, GCF of Fractions is 2/5778.Finally, GCF of Fractions for 7744/54, 9942/214 is 2/5778.